FORT HOOD, Texas (Reuters) - Jury selection was completed on Tuesday for the military murder trial of an Army Major accused of killing 13 soldiers at Fort Hood, Texas in 2009, the biggest non-combat massacre on a U.S. base.

Military judge Colonel Tara Osborn said on Tuesday that three more members of the jury had been confirmed after 10 U.S. Army officers were chosen last week for the court martial of Major Nidal Hasan, an Army psychiatrist. Opening statements are scheduled to begin no earlier than August 6.

Hasan has said he opened fire on November 5, 2009 to protect Muslims and the Taliban in Afghanistan from aggression by the United States. He was shot by civilian base police during the attack and is paralyzed from the chest down.

Fort Hood was a major deployment point for the wars in Iraq and Afghanistan. At the time of the shooting Hasan, an American-born Muslim, was preparing to deploy to Afghanistan with a unit assigned to help soldiers deal with mental health issues.

Witnesses say Hasan shouted in Arabic "God is greatest" while firing the gun. He has told the court he spends hours reading the Koran in his cell every day.

Hasan faces the death penalty if convicted of killing the soldiers and wounding 32 other people when he opened fire at a Fort Hood facility where soldiers prepare for deployments.

The 13 jurors, all of whom are of superior rank to Hasan, will be asked to decide if he is guilty of premeditated murder and premeditated attempted murder. They must be unanimous to impose a death sentence. The last court martial execution in the United States was in 1961.

Hasan could also be sentenced to life without parole, or be found guilty on lesser charges.

The Army has not released the names of the jurors who include 10 colonels, two lieutenant colonels and a major.

The case has been delayed several times by unusual turns including arguments over whether Hasan could keep a beard against Army regulations and whether he could represent himself in the court martial. He is representing himself.

Hasan has been allowed to wear the beard, which he said he grew for religious reasons, and in court is wearing a combat camouflage uniform, rather than a dress uniform, for medical reasons.